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Last updated on May 26th, 2025

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Square Root of 2340

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If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 2340.

Square Root of 2340 for Australian Students
Professor Greenline from BrightChamps

What is the Square Root of 2340?

The square root is the inverse operation of squaring a number. 2340 is not a perfect square. The square root of 2340 can be expressed in both radical and exponential forms. In radical form, it is expressed as √2340, whereas in exponential form, it is written as (2340)^(1/2). The square root of 2340 is approximately 48.377, which is an irrational number because it cannot be expressed as a ratio of two integers.

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Finding the Square Root of 2340

The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 2340, methods such as the long division method and approximation method are used. Let us now learn about these methods: 

 

  • Prime factorization method 
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 2340 by Prime Factorization Method

The prime factorization of a number is the product of its prime factors. Let's look at how 2340 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 2340 Breaking it down, we have 2 × 2 × 3 × 3 × 5 × 13: 2^2 × 3^2 × 5 × 13

 

Step 2: Now that we have found the prime factors of 2340, the next step is to make pairs of those prime factors. Since 2340 is not a perfect square, the digits of the number cannot be fully paired. Therefore, calculating 2340 using prime factorization to find its square root involves taking the square roots of the pairs and any remaining factors.

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Square Root of 2340 by Long Division Method

The long division method is particularly useful for finding the square root of non-perfect square numbers. Here is how you can find the square root of 2340 using the long division method, step by step:

 

Step 1: Group the numbers from right to left. In the case of 2340, group it as 23 and 40.

 

Step 2: Find the largest number whose square is less than or equal to 23. This is 4, since 4^2 = 16. The quotient is 4, and after subtracting, the remainder is 7.

 

Step 3: Bring down the next pair of digits, 40, making the new dividend 740.

 

Step 4: Double the quotient to get the new divisor, which is 8. Find the largest digit x such that 8x × x ≤ 740.

 

Step 5: Through trial and error, find that 8 × 9 = 72 and 9 × 9 = 81; 729 is the closest number under 740.

 

Step 6: Subtract 729 from 740 to get a remainder of 11.

 

Step 7: Add a decimal point to the quotient and bring down pairs of zeroes to continue the division to get more decimal places in the square root. Continue this process until you have the desired precision for the square root of 2340, which is approximately 48.377.

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Square Root of 2340 by Approximation Method

The approximation method is another way to find square roots. It is a straightforward method to estimate the square root of a given number. Here’s how to find the square root of 2340 using the approximation method:

 

Step 1: Identify the perfect squares between which 2340 lies. The perfect squares closest to 2340 are 2304 (48^2) and 2401 (49^2). Therefore, √2340 falls between 48 and 49.

 

Step 2: Use the formula to approximate the decimal: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square)

 

Step 3: Apply the formula: (2340 - 2304) / (2401 - 2304) = 36 / 97 ≈ 0.371 Add this to the smaller perfect square root: 48 + 0.371 = 48.371 Therefore, the square root of 2340 is approximately 48.371.

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Common Mistakes and How to Avoid Them in the Square Root of 2340

Students often make mistakes while finding square roots, such as forgetting about the negative square root or mishandling the long division method. Let’s look at a few common mistakes in detail.

Mistake 1

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Forgetting about the Negative Square Root

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It is important for students to know that every positive number has both positive and negative square roots. However, we usually focus on the principal (positive) square root in practical scenarios.

For example, √50 = ±7.071, but we often use the positive root.

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Square Root of 2340 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √2340?

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The area of the square box is approximately 2340 square units.

Explanation

The area of a square is calculated as side^2.

If the side length is √2340, then the area is (√2340) × (√2340) = 2340.

Thus, the area of the square box is 2340 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 2340 square feet is built; if each side measures √2340, what will be the square feet of half of the building?

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1170 square feet.

Explanation

Since the building is square-shaped, divide the total area by 2 to find half the area: 2340 ÷ 2 = 1170.

Thus, half of the building measures 1170 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √2340 × 5.

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Approximately 241.885.

Explanation

First, find the square root of 2340, which is approximately 48.377.

Then multiply this value by 5: 48.377 × 5 ≈ 241.885.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (2340 + 60)?

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Approximately 49.497.

Explanation

First, find the sum of 2340 and 60, which is 2400.

Then, find the square root of 2400, which is approximately 49.497.

Therefore, the square root of (2340 + 60) is approximately ±49.497.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √2340 units and the width ‘w’ is 40 units.

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The perimeter of the rectangle is approximately 176.754 units.

Explanation

Perimeter of a rectangle = 2 × (length + width).

Perimeter = 2 × (√2340 + 40) = 2 × (48.377 + 40) = 2 × 88.377 ≈ 176.754 units.

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FAQ on Square Root of 2340

1.What is √2340 in its simplest form?

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2.Mention the factors of 2340.

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3.Calculate the square of 2340.

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4.Is 2340 a prime number?

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5.2340 is divisible by?

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6.How does learning Algebra help students in Australia make better decisions in daily life?

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7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 2340?

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8.How do technology and digital tools in Australia support learning Algebra and Square Root of 2340?

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9.Does learning Algebra support future career opportunities for students in Australia?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 2340

  • Square Root: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16.

 

  • Irrational Number: An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers. Its decimal form is non-repeating and non-terminating.

 

  • Perfect Square: A perfect square is an integer that is the square of another integer. For example, 36 is a perfect square because it is 6^2.

 

  • Long Division Method: A method used to find the square root of non-perfect squares by approximating the value through a series of division and subtraction steps.

 

  • Decimals: Numbers that include a decimal point to represent a fraction of a whole number, e.g., 3.14, 0.5, etc.
Professor Greenline from BrightChamps

About BrightChamps in Australia

At BrightChamps, we believe algebra is more than symbols—it opens doors to endless opportunities! Our mission is to help children all over Australia gain important math skills, focusing today on the Square Root of 2340 with a special emphasis on understanding square roots—in a lively, fun, and easy-to-grasp way. Whether your child is calculating the speed of a roller coaster at Luna Park Sydney, tracking cricket match scores, or managing their allowance for the newest gadgets, mastering algebra gives them the confidence to tackle everyday problems. Our interactive lessons make learning both simple and enjoyable. Since children in Australia learn in various ways, we adapt our approach to fit each learner’s style. From Sydney’s vibrant streets to the stunning Gold Coast beaches, BrightChamps brings math to life, making it relevant and exciting throughout Australia. Let’s make square roots a joyful part of every child’s math journey!
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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